How does one create a non-classifying CNN in order to gain information from images?
This can be thought of as a loss function design problem. If you optimize your network weights for something like multi-class classification, then expect your network to learn weights for this task (You will use cross entropy loss for this task). If you optimize your network to output a single value at the last layer and treat it as a regression problem for age prediction, then your network can learn weights for this particular task (You may use something like Mean Square Error loss here).

Let me give you a weak guidline on how to do this. Suppose say your input is images of chairs and you want to predict their age using a pretrained resnet, this is how you may do it in pytorch.

Definition
X: Input pictures
Y: List of ground truth values which is age here. i.e. : [1.4, 2.5, 2.2, ....]  

Modify your neural network to give one output at the last layer
model = torchvision.models.resnet18(pretrained=True)
num_ftrs = model.fc.in_features
model.fc = torch.nn.Linear(num_ftrs, 1)  

Design your loss function appropriately. You can treat age prediction as a standard regression problem. Of course, there are better loss designs here.
criterion =  torch.nn.MSELoss()

So use this loss during training
loss = criterion(output, target) where output is your neural network prediction and target is your ground truth values.

This is how you can modify an existing architecture for your task. Hope it helps.